Power statistics-equivalent finite groups
This article defines an equivalence relation over the collection of groups. View a complete list of equivalence relations on groups.
Relation with group properties
Note that the third column (first question column) is the conjunction of the fourth and fifth columns.
|Group property||Finite version||Is any group power statistics-equivalent to a group with this property isomorphic to it?||Does any group power statistics-equivalent to a group with this property also have this property?||Are any two groups with this property that are power statistics-equivalent also isomorphic?|
|Cyclic group||Finite cyclic group||Yes||Yes||Yes|
|Abelian group||Finite abelian group||No||No||Yes: Finite abelian groups with the same power statistics are isomorphic|
|Nilpotent group||Finite nilpotent group||No||?||No|